In [1]}, I noted that this implies for any symmetrically normed trace ideal, \({\mathcal {I}}_\Phi \) , that
\( e^{-A/2} e^{-B} e^{-A/2} \in {\mathcal {I}}_\Phi \Rightarrow e^{-(A+B)}\in {\mathcal {I}}_\Phi \) 
